At #8 of the count down of the Ten Greatest Warriors of the Westeros we go from Robert Baratheon, the King at #9, to perhaps one of the most base-born characters in the books: Bronn. Before I get into it I know there is a huge faction who thinks he is the greatest warriors ever in the books. I don't agree with this, see below for why. I think some of the appeal is the ant-hero vibe that is so prevalent today. Great, he's an anti-hero, doesn't mean he's "better". And as we go to through the list I don't think Bronn could win with the likes of #1-5, but more on them later.
The lean, mean, two-fisted warrior of the Westeros makes the list, cool. When we first meet him its during a Caetlyn chapter in A Game of Throne, when she hauls the Imp to the Aerie of the Vale. Being the smart sort Tyrion demands trial by combat and Bronn steps up against Ser Vardis Egen which he easily slays winning Tyrion's freedom. Getting their he helped repel an assault of the Mountain Men as well.
Bronn is certainly not the strongest warrior and perhaps not even the quickest warrior in the books. What Bronn probably is: one of the, if not the smartest warriors in the books. Bronn above all else survives and he does this by knowing when and how to fight, but even more importantly when not to fight. Only he and the Red Viper are not intimidated by the Mountain that Rides (at least as far as we the readers know) and tells Tyrion how he could be defeated. It's also telling that he declines to champion Tyrion (a second time in fact) this time around against likes of Gregor rather then an over-matched Ser Vardis Egen; that's where the Red Viper steps in. Not that he's afraid mind you, it's there is nothing in it for him. That is probably Bronn's biggest strength: he fights for nothing, if nothing can be gained.
It's important to note that he is not above tricks and dirty ones at that. As a sellsword he is agile and fights with less armor then most. Sometimes he fights with two weapons so we can be pretty sure of his skill. Above all he is practical, formality means nothing to him. In that sense he's the exact opposite of The Knight of Flowers.
Bronn so far has not really beaten anyone that could be called dangerous. Dangerous in the sense that he is really going to have a hard time dispatching them. Bronn is too smart for that; one could say however that he only fights foes he is sure that he can beat as well as if there is something in it for him.
Bronn is brave, but his survival instinct makes him a curious case. The interesting thing is that fact that he fought well at the Battle Blackwater. Clearly he could have slipped away, but there he was leading sorties along with the Hound.
Again, in closing: I personally have nothing against Bronn. Bronn is probably not the best warrior in the Westeros (hey he made the list), but he is probably #1 or 2 when it comes to smarts as a warrior. He has a critical eye to see the weakness of his foe and capitalize on them. That's why he is here, against some of the later that will appear on this list his smarts would probably not save him.